Pay for the survey, $700 is probably a good price, so I'd do it. Surveying has a lot of 'art' and nuance to it as well as the mathematical component. I work as a civil, but have survey support experience as well.
I currently have a client who is looking to buy a parcel it's around 1 acre. The west and possibly north boundary of the lot have a 1-1.5' gap and an 18' "shift" to the east. Also the course decribing the lot doesn't close by 35'...three parcels adjacent to ours that we share a boundary with have completed record surveys over the last 40 years and have identified and attempted to reconcile the issues using good survey theories (the art behind the math, who gets what and by how much and why). The problem is taking them collectively results in new problems for our lot...the three solutions work when you look at just one of our shared lines, but when you look at all three the math falls apart...my surveyor will have to take their collective work, his new field investigation and then apply his own good theories, and hopefully our property is the missing piece in the puzzle for how to resolve this.
I share that because those three surveyors are all names I or my boss know, and do good work. Their work isn't low quality but I disagree with some of the conclusions they came to in determining boundaries that are adjacent to ours...if I just went and marked their pins my client could 'lose' 18'-35' of their property...or almost worse, build 18' too close to the street ROW likely putting their house into the City easement...